相关论文: Derivative expansion in a two-scalar field theory

A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations…

We use a generalised real-time path formalism with properly regularised propagators based on Le Bellac and Mabilat \cite{belmab} and calculate the effective potential and the higher order derivative terms of the effective action in the case…

A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…

We study the one-loop quantum corrections for higher-derivative superfield theories, generalizing the approach for calculating the superfield effective potential. In particular, we calculate the effective potential for two versions of…

We discuss the phase structure of a higher derivative four-fermion model in four dimensions in curved spacetime in frames of the $\frac{1}{N_c}$-expansion. First, we evaluate in our model the effective potential of two composite scalars in…

The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…

Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…

Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…

In this work, we systematically analyze higher derivative terms in the supersymmetric effective actions for three dimensional scalar field theories using $\mathcal{N} =1$ superspace formalism. In these effective actions, we show that…

A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.

The perturbative dynamics of quantum field theories is described by a recursive expansion similar to the well known loop expansion. The equivalent formulation based on low-energy dynamics via an expansion in derivatives is well known in the…

This thesis introduces an effective theory for the long-distance behaviour of scalar fields in de Sitter spacetime, known as the second-order stochastic theory, with the aim of computing scalar correlation functions that are useful in…

A derivative expansion of the Wegner-Houghton equation is derived for a scalar theory. The corresponding full non-perturbative renormalization group equations for the potential and the wave-function renormalization function are presented.…

The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar…

We obtain a derivative formula for various notions of capacity. Namely we identify the second order term in the asymptotic expansion of the capacity of a union of two sets, as their distance goes to infinity. Our result applies to the usual…

The correct quantum description for a curvature squared term in the action can be obtained by casting the action in the canonical form with the introduction of a variable which is the negative of the first derivative of the field variable…

We consider a second order linear evolution equation with a dissipative term multiplied by a time-dependent coefficient. Our aim is to design the coefficient in such a way that all solutions decay in time as fast as possible. We discover…

In this paper, we discuss the dynamics of two- scalar-field cosmological models. Unlike in the situation of exponential potential, we find that there are late-time attractors in which one scalar field dominates the energy density of…

The effective equation of motion is derived for a scalar field interacting with other fields in a Friedman-Robertson-Walker background space-time. The dissipative behavior reflected in this effective evolution equation is studied both in…

We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using…